The second "了" is not necessary here. If you remove it, the same meaning can still be conveyed. If you really want to know what the meaning is, I would say that the second "了" is just to emphasize that this action is done. Actually, it sounds better to me without the second "了". Hope my explanation helps you. :) ---Jill

first shows the past tense, second -- the change of the situation

Well, judging by two "了" in this sentence, we can assume that the context is: someone else brought me a same sweater as the one "he" had brought me already,

you should know two things: 1) verb + 了 = past tense so, he bought this sweater for me = 他给我买了这件毛衣。 2) if we put a "了" at the end of a phrase, it means that something new happened or something new will happen. for example, 下雨了 (happened) 就要下雨了 (will happen) anyway, in this case, 了 emphasizes some change, it expresses some emotion of speaker. so for your example: 他给我买了这件毛衣了, the second 了 tells us that you are trying to express some emotion. maybe someone is asking you like this: didn't he buy this sweater for you? or maybe “他” bought you this sweater to surprise you and now you are telling us about that. Anyway, the second 了 tells us that you are trying to emphasize the change: from "you have no sweater" to "you have it".

他给我买了这件毛衣了。=他给我买过这件毛衣了。 When I read it aloud, I realize that the speaker may complain "He gave me this sweater, why did you do it again?"